The Torsion of the Group of Homeomorphisms of Powers of the Long Line

Satya Deo and David Gauld


By blending techniques from Set Theory and Algebraic Topology we investigate the order of any
homeomorphism of the $n$th power of the long ray or long line $L$ having finite order, finding
all possible orders when $n=1, 2, 3$ or 4 in the first case and when $n=1$ or 2 in the second. We
also show that all finite powers of $L$ are acyclic with respect to Alexander-Spanier cohomology.

long line, long ray, Alexander-Spanier cohomology, torsion of homeomorphisms

Math Review Classification
Primary 55M35 ; Secondary 57N65, 57N80, 57S17, 03E75

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14 pages

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